Finite Group Databasebeta

← #356490

Subgroups — #356490

Order 512.

2810 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2342C211yesmaximal, characteristic
2C2×#2342C212yesmaximal
3C2×#1740C211yesmaximal, characteristic, complemented
4C22×#342C211yesmaximal, characteristic
5#10854C212yesmaximal, complemented
6#10846C211yesmaximal, characteristic, complemented
7#10736C212yesmaximal, complemented
8#10735C212yesmaximal
9#10726C211yesmaximal, characteristic, complemented
10#10725C211yesmaximal, characteristic
11C4×#342C211yesmaximal, characteristic, complemented
12C22×#117C2212yes—
13C22×#117C2211yescharacteristic
14C23×C22⋊C4C2211yescharacteristic
15C23×C22⋊C4C2212yes—
16C23×C22⋊C4C2211yescharacteristic
17#2342—28no—
18#2342—22no—
19#2342—22no—
20#2342—22no—
21#2342—22no—
22#2342C4116yescomplemented
23C2×#388—22no—
24C2×#388—22no—
25C2×#388C412yescomplemented
26C2×#388C412yescomplemented
27C2×#385—22no—
28C2×#385C412yescomplemented
29C2×#381C2212yes—
30C2×#381C2211yescharacteristic
31C2×#380C2212yes—
32C2×#380C2211yescharacteristic
33C2×#379C2212yes—
34C2×#379C2211yescharacteristic
35C2×C4×C22⋊C4—22no—
36C2×C4×C22⋊C4C412yescomplemented
37C2×C4×C22⋊C4C2212yes—
38C2×C4×C22⋊C4C2211yescharacteristic
39#1740—24no—
40C2×#342—24no—
41C2×#342C2211yescharacteristic
42C2×#342C2211yescharacteristic
43C2×#342C2212yes—
44C2×#342C2212yes—
45C2×#342C2211yescharacteristic
46C2×#342C2212yes—
47C2×#342C2212yes—
48C2×#342C2212yes—
49C2×#342C2212yes—
50C2×#342C2211yescharacteristic
51C26C2311yescharacteristic
52C24×C4—22no—
53C24×C4C2×C412yes—
54C24×C4C2311yescharacteristic
55C24×C4C2311yescharacteristic
56C2×#117—22no—
57C2×#117—22no—
58C2×#117—24no—
59C2×#117—22no—
60C2×#117—22no—
61C2×#117—24no—
62C2×#117—24no—
63C2×#117—42no—
64C2×#117—42no—
65C2×#117—42no—
66C2×#117C2×C418yescomplemented
67C22×C4⋊C4—22no—
68C22×C4⋊C4—22no—
69C22×C4⋊C4C2×C412yescomplemented
70C22×C4⋊C4C2×C412yescomplemented
71C22×C22⋊C4—24no—
72C22×C22⋊C4—24no—
73C22×C22⋊C4—22no—
74C22×C22⋊C4—22no—
75C22×C22⋊C4—24no—
76C22×C22⋊C4—22no—
77C22×C22⋊C4—22no—
78C22×C22⋊C4—22no—
79C22×C22⋊C4—22no—
80C22×C22⋊C4—22no—
81C22×C22⋊C4—42no—
82C22×C22⋊C4—42no—
83C22×C22⋊C4—42no—
84C22×C22⋊C4C2×C412yes—
85C22×C22⋊C4C2×C418yes—
86C22×C22⋊C4C2×C412yes—
87C22×C22⋊C4C2×C412yes—
88C22×C22⋊C4C2×C418yes—
89C22×C22⋊C4C2×C411yescharacteristic
90C22×C22⋊C4C2×C411yescharacteristic
91C22×C22⋊C4C2×C411yescharacteristic
92C22×C22⋊C4C2×C411yescharacteristic
93C22×C22⋊C4D414yes—
94C22×C22⋊C4D412yes—
95C22×C22⋊C4D412yes—
96C22×C22⋊C4D412yes—
97C22×C22⋊C4D412yes—
98C22×C22⋊C4Q814yes—
99C22×C22⋊C4C2311yescharacteristic
100C22×C22⋊C4C2311yescharacteristic
101C22×C22⋊C4C2311yescharacteristic
102C22×C22⋊C4C2312yes—
103C22×C22⋊C4C2312yes—
104C22×C22⋊C4C2312yes—
105C22×C22⋊C4C2311yescharacteristic
106C22×C22⋊C4C2312yes—
107C22×C42—22no—
108C22×C42—22no—
109C22×C42C2×C412yescomplemented
110C22×C42C2×C412yescomplemented
111#388—24no—
112#388—24no—
113#388—24no—
114#388—24no—
115#388—216no—
116#388—216no—
117#385—24no—
118#385—24no—
119#385—216no—
120#381—24no—
121#381—22no—
122#381—22no—
123#381C2×C418yescomplemented
124#380—24no—
125#380—22no—
126#380—22no—
127#380C2×C418yescomplemented
128#379—24no—
129#379—22no—
130#379—22no—
131#379C2×C418yes—
132C4×C22⋊C4—24no—
133C4×C22⋊C4—22no—
134C4×C22⋊C4—22no—
135C4×C22⋊C4—22no—
136C4×C22⋊C4—22no—
137C4×C22⋊C4—22no—
138C4×C22⋊C4—22no—
139C4×C22⋊C4—216no—
140C4×C22⋊C4C2×C418yescomplemented
141C2×#95—22no—
142C2×#95—22no—
143C2×#95—22no—
144C2×#95—22no—
145C2×#95C2×C412yescomplemented
146C2×#95C2×C412yescomplemented
147C2×#95C2×C412yescomplemented
148C2×#95C2×C412yescomplemented
149#342—22no—
150#342—24no—
151#342—22no—
152#342—24no—
153#342—22no—
154#342—24no—
155#342—42no—
156#342—42no—
157#342—42no—
158#342D414yes—
159C25—21no—
160C25—21no—
161C25—22no—
162C25—22no—
163C25—21no—
164C25—21no—
165C25—44no—
166C25—82no—
167C25C22×C411yescharacteristic
168C25C22×C411yescharacteristic
169C25C22×C414yes—
170C25C2×D412yes—
171C25C2×D412yes—
172C25C2×D412yes—
173C25C2×Q812yes—
174C25C2411yescharacteristic
175C23×C4—21no—
176C23×C4—21no—
177C23×C4—22no—
178C23×C4—22no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—22no—
182C23×C4—22no—
183C23×C4—22no—
184C23×C4—22no—
185C23×C4—22no—
186C23×C4—22no—
187C23×C4—28no—
188C23×C4—24no—
189C23×C4—42no—
190C23×C4—44no—
191C23×C4—44no—
192C23×C4—48no—
193C23×C4—44no—
194C23×C4—82no—
195C23×C4—84no—
196C23×C4—82no—
197C23×C4C22×C411yescharacteristic
198C23×C4C22×C414yes—
199C23×C4C22×C411yescharacteristic
200C23×C4C22×C412yes—
201C23×C4C22×C412yes—
202C23×C4C22×C412yes—
203C23×C4C22×C412yes—
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C414yes—
207C23×C4C2×D412yes—
208C23×C4C2×D412yes—
209C23×C4C2×D412yes—
210C23×C4C2×D412yes—
211C23×C4C2×D412yes—
212C23×C4C2×D412yes—
213C23×C4C2×Q812yes—
214C23×C4C2×Q812yes—
215#117—216no—
216#117—48no—
217#117—44no—
218#117—44no—
219#117—44no—
220#117—44no—
221#117—48no—
222#117—48no—
223C2×C4⋊C4—28no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—42no—
229C2×C4⋊C4—44no—
230C2×C4⋊C4—44no—
231C2×C4⋊C4—84no—
232C2×C4⋊C4—82no—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4—22no—
248C2×C22⋊C4—22no—
249C2×C22⋊C4—22no—
250C2×C22⋊C4—216no—
251C2×C22⋊C4—28no—
252C2×C22⋊C4—24no—
253C2×C22⋊C4—28no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—22no—
258C2×C22⋊C4—22no—
259C2×C22⋊C4—21no—
260C2×C22⋊C4—22no—
261C2×C22⋊C4—22no—
262C2×C22⋊C4—22no—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—21no—
266C2×C22⋊C4—22no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—24no—
272C2×C22⋊C4—28no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—48no—
275C2×C22⋊C4—48no—
276C2×C22⋊C4—44no—
277C2×C22⋊C4—44no—
278C2×C22⋊C4—48no—
279C2×C22⋊C4—44no—
280C2×C22⋊C4—44no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—44no—
283C2×C22⋊C4—44no—
284C2×C22⋊C4—48no—
285C2×C22⋊C4—44no—
286C2×C22⋊C4—84no—
287C2×C22⋊C4—82no—
288C2×C22⋊C4C4214yes—
289C2×C22⋊C4C4214yes—
290C2×C22⋊C4C4214yes—
291C2×C22⋊C4C4214yes—
292C2×C22⋊C4C22⋊C418yes—
293C2×C22⋊C4C22⋊C411yescharacteristic
294C2×C22⋊C4C22⋊C411yescharacteristic
295C2×C22⋊C4C22⋊C411yescharacteristic
296C2×C22⋊C4C22⋊C411yescharacteristic
297C2×C22⋊C4C22⋊C418yes—
298C2×C22⋊C4C22⋊C412yes—
299C2×C22⋊C4C22⋊C412yes—
300C2×C22⋊C4C22⋊C418yes—
301C2×C22⋊C4C22⋊C418yes—
302C2×C22⋊C4C22⋊C412yes—
303C2×C22⋊C4C22⋊C412yes—
304C2×C22⋊C4C22⋊C412yes—
305C2×C22⋊C4C22⋊C412yes—
306C2×C22⋊C4C4⋊C418yes—
307C2×C22⋊C4C4⋊C418yes—
308C2×C22⋊C4C4⋊C414yes—
309C2×C22⋊C4C4⋊C414yes—
310C2×C22⋊C4C4⋊C418yes—
311C2×C22⋊C4C4⋊C418yes—
312C2×C22⋊C4C4⋊C414yes—
313C2×C22⋊C4C4⋊C414yes—
314C2×C22⋊C4C22×C414yes—
315C2×C22⋊C4C22×C414yes—
316C2×C22⋊C4C22×C414yes—
317C2×C22⋊C4C22×C414yes—
318C2×C22⋊C4C2×D412yes—
319C2×C22⋊C4C2×D414yes—
320C2×C22⋊C4#4112yes—
321C2×C22⋊C4#4114yes—
322C2×C42—22no—
323C2×C42—22no—
324C2×C42—28no—
325C2×C42—24no—
326C2×C42—22no—
327C2×C42—22no—
328C2×C42—28no—
329C2×C42—42no—
330C2×C42—44no—
331C2×C42—44no—
332C2×C42—84no—
333C2×C42—82no—
334#95—28no—
335#95—28no—
336#95—28no—
337#95—28no—
338#95—22no—
339#95—22no—
340#95—22no—
341#95—22no—
342#95—24no—
343#95—24no—
344C24—21no—
345C24—21no—
346C24—21no—
347C24—21no—
348C24—22no—
349C24—22no—
350C24—22no—
351C24—22no—
352C24—24no—
353C24—28no—
354C24—21no—
355C24—24no—
356C24—21no—
357C24—24no—
358C24—21no—
359C24—24no—
360C24—21no—
361C24—24no—
362C24—22no—
363C24—22no—
364C24—22no—
365C24—24no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—24no—
372C24—42no—
373C24—44no—
374C24—42no—
375C24—42no—
376C24—42no—
377C24—44no—
378C24—42no—
379C24—48no—
380C24—44no—
381C24—44no—
382C24—44no—
383C24—84no—
384C24—82no—
385C24—82no—
386C24—84no—
387C24—84no—
388C24—88no—
389C24—88no—
390C24—84no—
391C24—84no—
392C24C2×C4212yes—
393C24C2×C4212yes—
394C24C2×C22⋊C412yes—
395C24C2×C22⋊C411yescharacteristic
396C24C2×C22⋊C414yes—
397C24C2×C22⋊C411yescharacteristic
398C24C2×C22⋊C414yes—
399C24C2×C4⋊C412yes—
400C24C2×C4⋊C414yes—
401C24C2×C4⋊C412yes—
402C24C2×C4⋊C414yes—
403C24C23×C411yescharacteristic
404C24C23×C412yes—
405C24C22×D412yes—
406C24C22×D411yescharacteristic
407C24C22×D411yescharacteristic
408C24C22×Q811yescharacteristic
409C24C2×#4111yescharacteristic
410C24C2×#4112yes—
411C24H(5,𝔽2)12yes—
412C24H(5,𝔽2)11yescharacteristic
413C242−1+411yescharacteristic
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—24no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—24no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—42no—
458C22×C4—44no—
459C22×C4—42no—
460C22×C4—44no—
461C22×C4—416no—
462C22×C4—44no—
463C22×C4—44no—
464C22×C4—44no—
465C22×C4—44no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—44no—
469C22×C4—44no—
470C22×C4—44no—
471C22×C4—44no—
472C22×C4—44no—
473C22×C4—416no—
474C22×C4—44no—
475C22×C4—44no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—44no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—42no—
489C22×C4—84no—
490C22×C4—82no—
491C22×C4—82no—
492C22×C4—82no—
493C22×C4—82no—
494C22×C4—88no—
495C22×C4—88no—
496C22×C4—816no—
497C22×C4—816no—
498C22×C4—88no—
499C22×C4C2×C4212yes—
500C22×C4C2×C4212yes—
501C22×C4C2×C4212yes—
502C22×C4C2×C4212yes—
503C22×C4C2×C22⋊C414yes—
504C22×C4C2×C22⋊C414yes—
505C22×C4C2×C22⋊C411yescharacteristic
506C22×C4C2×C22⋊C411yescharacteristic
507C22×C4C2×C22⋊C411yescharacteristic
508C22×C4C2×C22⋊C411yescharacteristic
509C22×C4C2×C22⋊C412yes—
510C22×C4C2×C22⋊C412yes—
511C22×C4C2×C22⋊C414yes—
512C22×C4C2×C22⋊C414yes—
513C22×C4C2×C4⋊C412yes—
514C22×C4C2×C4⋊C414yes—
515C22×C4C2×C4⋊C414yes—
516C22×C4C2×C4⋊C412yes—
517C22×C4C2×C4⋊C412yes—
518C22×C4C2×C4⋊C412yes—
519C22×C4C2×C4⋊C414yes—
520C22×C4C2×C4⋊C414yes—
521C22×C4C4×D414yes—
522C4⋊C4—48no—
523C4⋊C4—416no—
524C4⋊C4—84no—
525C4⋊C4—88no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—24no—
537C22⋊C4—48no—
538C22⋊C4—416no—
539C22⋊C4—416no—
540C22⋊C4—44no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—44no—
554C22⋊C4—84no—
555C22⋊C4—88no—
556C22⋊C4#9518yes—
557C22⋊C4#9514yes—
558C22⋊C4#9514yes—
559C22⋊C4#9518yes—
560C22⋊C4#9518yes—
561C22⋊C4#9518yes—
562C22⋊C4#9518yes—
563C22⋊C4#9514yes—
564C22⋊C4#9514yes—
565C22⋊C4#9518yes—
566C22⋊C4C4×D418yes—
567C42—44no—
568C42—44no—
569C42—416no—
570C42—82no—
571C42—82no—
572C42—88no—
573C23—21no—
574C23—21no—
575C23—22no—
576C23—24no—
577C23—22no—
578C23—24no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—21no—
583C23—24no—
584C23—21no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—22no—
589C23—24no—
590C23—22no—
591C23—24no—
592C23—24no—
593C23—22no—
594C23—28no—
595C23—24no—
596C23—24no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—24no—
601C23—24no—
602C23—22no—
603C23—24no—
604C23—22no—
605C23—24no—
606C23—22no—
607C23—22no—
608C23—44no—
609C23—42no—
610C23—41no—
611C23—41no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—44no—
618C23—42no—
619C23—42no—
620C23—44no—
621C23—44no—
622C23—42no—
623C23—42no—
624C23—44no—
625C23—42no—
626C23—44no—
627C23—42no—
628C23—44no—
629C23—42no—
630C23—42no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—48no—
635C23—48no—
636C23—48no—
637C23—44no—
638C23—44no—
639C23—48no—
640C23—82no—
641C23—82no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—82no—
646C23—82no—
647C23—84no—
648C23—88no—
649C23—88no—
650C23—88no—
651C23—88no—
652C23—84no—
653C23—88no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—88no—
658C23C2×#9512yes—
659C23C2×#9514yes—
660C23C2×#9512yes—
661C23#41014yes—
662C23C22×C4211yescharacteristic
663C23C22×C22⋊C412yes—
664C23C22×C22⋊C411yescharacteristic
665C23C22×C4⋊C411yescharacteristic
666C23C22×C4⋊C412yes—
667C23C2×C4×D411yescharacteristic
668C23C2×C4×D412yes—
669C23C4×#4111yescharacteristic
670C23C4×#4112yes—
671C23#51811yescharacteristic
672C23#51812yes—
673C23#52011yescharacteristic
674C23#52012yes—
675C23D4212yes—
676C23D4211yescharacteristic
677C23#54612yes—
678C23#54612yes—
679C23#54612yes—
680C23#54712yes—
681C23#54711yescharacteristic
682C23D4×Q811yescharacteristic
683C23#55411yescharacteristic
684C23#55412yes—
685C2×C4—24no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—28no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—48no—
723C2×C4—48no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—88no—
747C2×C4—832no—
748C2×C4—88no—
749C2×C4—84no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4—84no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—82no—
760C2×C4—82no—
761C2×C4C2×#9512yes—
762C2×C4C2×#9512yes—
763C2×C4C2×#9514yes—
764C2×C4C2×#9512yes—
765C2×C4C2×#9514yes—
766C2×C4C2×#9512yes—
767C22—22no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—22no—
772C22—21no—
773C22—22no—
774C22—21no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—22no—
783C22—22no—
784C22—24no—
785C22—24no—
786C22—22no—
787C22—22no—
788C22—24no—
789C22—24no—
790C22—22no—
791C22—24no—
792C22—22no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—48no—
804C22—48no—
805C22—44no—
806C22—48no—
807C22—44no—
808C22—48no—
809C22—44no—
810C22—44no—
811C22—42no—
812C22—44no—
813C22—42no—
814C22—44no—
815C22—84no—
816C22—84no—
817C22—82no—
818C22—84no—
819C22—82no—
820C22—84no—
821C22—82no—
822C22—82no—
823C22#174014yescomplemented
824C22C22×#9511yescharacteristic
825C22C42×D411yescharacteristic
826C22#227511yescharacteristic
827C22D4×C22⋊C412yes—
828C22D4×C22⋊C411yescharacteristic
829C22#233912yes—
830C22#233911yescharacteristic
831C22D4×C4⋊C411yescharacteristic
832C22D4×C4⋊C412yes—
833C22#234911yescharacteristic
834C22#234912yes—
835C22C2×#41012yes—
836C22#288312yes—
837C4—22no—
838C4—22no—
839C4—24no—
840C4—22no—
841C4—24no—
842C4—22no—
843C4—48no—
844C4—44no—
845C4—84no—
846C4—84no—
847C4—84no—
848C4—82no—
849C4—82no—
850C4—82no—
851C2—22no—
852C2—22no—
853C2—24no—
854C2—21no—
855C2—22no—
856C2—21no—
857C2—22no—
858C2—21no—
859C2—21no—
860C2—44no—
861C2—42no—
862C2D4×#9511yescharacteristic
863C2C2×#174011yescharacteristic
864C2#2035411yescharacteristic
865C2#2240512yes—
866C2#2247712yes—
subgroupG/H
center, socleC23C22×C22⋊C4
commutatorC23C22×C42
Frattini, cosocleC25C24
prime radicalC26C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C22⋊C4 ◁ G
LECSG ▷ C25 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#1740C2semidirect
5. #10854C2semidirect
6. #10846C2semidirect
7. #10736C2semidirect
9. #10726C2semidirect
11. C4×#342C2semidirect
22. #2342C4semidirect
25. C2×#388C4semidirect
26. C2×#388C4semidirect
28. C2×#385C4semidirect
36. C2×C4×C22⋊C4C4semidirect
66. C2×#117C2×C4semidirect
69. C22×C4⋊C4C2×C4semidirect
70. C22×C4⋊C4C2×C4semidirect
109. C22×C42C2×C4semidirect
110. C22×C42C2×C4semidirect
123. #381C2×C4semidirect
127. #380C2×C4semidirect
140. C4×C22⋊C4C2×C4semidirect
145. C2×#95C2×C4semidirect
146. C2×#95C2×C4semidirect
147. C2×#95C2×C4semidirect
148. C2×#95C2×C4semidirect
823. C22#1740semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#23422
C2×#17402
C22×#3422
#108542
#108462
#107362
#107352
#107262
#107252
C4×#3422